The couple – together for about 40 years after being introduced by mutual friend Jim Henson – announced the split at ABC’s summer press tour in Beverly Hills on Tuesday, releasing a joint statement on Twitter.

“After careful thought, thoughtful consideration and considerable squabbling, we have made the difficult decision to terminate our romantic relationship,” the estranged couple said. “We will continue to work together on television and in all media now known or hereafter devised, in perpetuity, throughout the universe. However, our personal lives are now distinct and separate, and we will be seeing other people, pigs, frogs, et al. This is our only comment on this private matter … unless we get the right offer. Thank you for your understanding.”

RELATED VIDEO: The Muppets Stars Kermit the Frog and Miss Piggy End Their 40 Year Relationship

If their press conference Tuesday is any indication, the TV and movie stars won’t behave as amicably as they’d hoped.

“It can be tough to work with your ex,” Kermit, 60, told the crowd. “It can be tough to be the executive producer on your ex s late-night TV show, especially when your ex is a pig. I don t know whether any of you have ever dated pigs.”

“One of us is certainly professional,” scoffed Piggy, 41. “”You can guess who that is, I’m sure. I have no problem working with my ex, okay? It’s fine. It’s totally healed.” She continued: “Dating moi is like flying close to the sun. It was inevitable that Kermit would drop down to the ground while I stayed in the heavens.”